We employ an alternative technique for determining the Lorentzian linewidth based upon the simultaneous measurement of the vapor transmission and group-velocity delay outside the Doppler core of an optically dense transition. We apply this technique to measure the cross sections for broadening of the intercombination lines of calcium, 4s 'S0~4s4p Pi, and strontium, Ss 'S0~5s5p Pi, by collisions with argon, neon and the ground-state neutral vapor. We compare our measured results with calculated values as well as previously determined values by other workers.PACS number(s): 32.70. Jz, 34.40.+n, 35.80.+s